Nabisco Hundred Calorie Packs

Nabisco Hundred Nabisco Hundred Calorie PacksCalorie Packs

Lorna Doone Short Bread CookiesLorna Doone Short Bread Cookies

Laurie Doyle, Beth Connolly, Helen Kushnir

Nabisco HistoryNabisco History

1898 New York Biscuit Company 1898 New York Biscuit Company by Adolphus Green and William by Adolphus Green and William MooreMoore

1906 moved headquarters from 1906 moved headquarters from Chicago to New YorkChicago to New York

Lorna Doone Short Bread Lorna Doone Short Bread Cookies first introduced in 1912 Cookies first introduced in 1912

Nabisco HistoryNabisco History

End of 1960’s leading cookie and End of 1960’s leading cookie and cracker manufacturer cracker manufacturer

1971 named Nabisco1971 named Nabisco 100 calorie packs now a $100 100 calorie packs now a $100

million brandmillion brand Over 30 different varietiesOver 30 different varieties

PurposePurpose

We are testing to see if each of the individual bags We are testing to see if each of the individual bags weigh the standard weight of 21 grams, as marked weigh the standard weight of 21 grams, as marked on the packages.on the packages.

We are also testing to see if the amount of cookies We are also testing to see if the amount of cookies present in each bag is the same, and that certain present in each bag is the same, and that certain bags don’t have more cookies than another.bags don’t have more cookies than another.

Making sure the consumer gets their money’s Making sure the consumer gets their money’s worth!worth!

We also want to make sure the weight isn’t over the We also want to make sure the weight isn’t over the expected amount so that there really is 100 calories expected amount so that there really is 100 calories in each bagin each bag

ProcedureProcedure Went to 7 different stores and purchased a box from Went to 7 different stores and purchased a box from

each store which allowed for a varied sample sizeeach store which allowed for a varied sample size The 7 stores were Acme, Genuardi’s, Giant, Rite Aid, Wegmans, The 7 stores were Acme, Genuardi’s, Giant, Rite Aid, Wegmans,

Target, and Shop Rite Target, and Shop Rite We randomly picked out a box from each store to We randomly picked out a box from each store to

purchasepurchase Allowed the samples to be more randomized Allowed the samples to be more randomized

Each box has 6 packages of cookies which allowed of a Each box has 6 packages of cookies which allowed of a total sample size of 42 packagestotal sample size of 42 packages

Counted and weighed the cookies from each of the 42 Counted and weighed the cookies from each of the 42 packages individually and recorded the results packages individually and recorded the results

Put the sample size together to compare our calculated Put the sample size together to compare our calculated weight with the expected weight of 21 g per package weight with the expected weight of 21 g per package

Used the cookie counts to calculate a 95% confidence Used the cookie counts to calculate a 95% confidence interval for the number of cookies per package interval for the number of cookies per package

785.s

42nMin: 20.04

Q1: 21.53

Med: 21.965

Q3: 22.25

Max: 24.06

8952.21x

Statistics for Statistics for GramsGrams

Box PlotBox PlotGrams per packageGrams per package

21.965 24.0620.04 22.2521.53

Weight in GramsWeight in Grams

Assumptions1. SRS

2. Normal Population or 30n

1.

2. 3042 n

One Sample t-One Sample t-TestTest

21: Ho

21: Ha

grams

grams

nsx

t

910325.2)41/3909.7( dfxp

7.3909

We reject Ho in favor of Ha because the p-value.05.10325.2 9 We have sufficient evidence that

the average amount of grams in one package of shortbread 100 calorie cookies is greater than 21 grams.

n

stx * ( 21.651, 22.14 )

We are 95% confident that the average number of We are 95% confident that the average number of grams per package is between 21.651 and 22.14 grams per package is between 21.651 and 22.14 grams.grams.

We reject Ho in favor of Ha because the expected We reject Ho in favor of Ha because the expected mean of 21 grams does not fall within the 95% mean of 21 grams does not fall within the 95% confidence interval. We have sufficient evidence that confidence interval. We have sufficient evidence that the average number of grams in a package is greater the average number of grams in a package is greater than 21 grams. than 21 grams.

One Sample t-One Sample t-Confidence Interval Confidence Interval

We took and SRS of five We took and SRS of five individual shortbread individual shortbread cookies and weighed cookies and weighed them. The average them. The average weight of one cookie was weight of one cookie was 1.04. We used the 1.04. We used the expected number of expected number of grams per package and grams per package and divided it by the average divided it by the average weight of a cookie to get weight of a cookie to get the expected number of the expected number of cookies per package. cookies per package.

cookiesgramsgrams 19.2004.121

20.1920.19 cookies is the cookies is the expected value per package.expected value per package.

Finding expected number Finding expected number of cookies per packageof cookies per package

95.19x

831.s42n

Min:18.25

Q1: 19

Med:20

Q3:20.5

Max:22

Statistics Statistics for Cookiesfor Cookies

Box PlotBox PlotCookies per packageCookies per package

20 20.5 221918.25

Number of CookiesNumber of Cookies

Assumptions

1. SRS

2. Normal Population or 30n

1.

2. 3042 n

One Sample t-One Sample t-TestTest

19.20: Ho cookies

19.20: Ha cookies

nsx

t

-1.8994

0323.)41/8994.1( dfxp

We reject Ho in favor of Ha because the p-value .0323 > . We have sufficient evidence that the mean number of cookies in a bag is less than 20.19.

05.

One Sample t-TestOne Sample t-Test

n

stx *( 19.687 , 20.205 )

We are 95% confident that the average number of grams We are 95% confident that the average number of grams per package is between 19.687 and 20.205 cookies.per package is between 19.687 and 20.205 cookies.

We fail to reject Ho in favor of Ha because the expected We fail to reject Ho in favor of Ha because the expected mean of 20.19 cookies falls within the 95% confidence mean of 20.19 cookies falls within the 95% confidence interval. We have sufficient evidence that the average interval. We have sufficient evidence that the average number of cookies in a package is equal to 20.19 number of cookies in a package is equal to 20.19 cookies. cookies.

One Sample t-One Sample t-Confidence Confidence

IntervalInterval

Scatter Plot

19202122232425

17 19 21 23

Weight

Nu

mb

er p

er

cookies

xy 7539.8586.6ˆ

7539.b8586.6a

7981.r

6369.2 r

Scatter PlotScatter Plot

6369.2 r

63.69% of the change in number of cookies per 63.69% of the change in number of cookies per package is determined by the change in package is determined by the change in weight.weight.

7539.bFor ever increase by one cookie, the weight For ever increase by one cookie, the weight increases by .7539 cookies.increases by .7539 cookies.

ApplicationApplication

The 100 calorie packs are often used in diets The 100 calorie packs are often used in diets so is important that each package truly has the so is important that each package truly has the amount of cookies it tell people it doesamount of cookies it tell people it does

All of us eat the 100 calories cookies and were All of us eat the 100 calories cookies and were interested in seeing how varied in weight and interested in seeing how varied in weight and count the packages really are count the packages really are

It allows us to test how true the company’s It allows us to test how true the company’s claim is of 21 grams of cookies per packageclaim is of 21 grams of cookies per package Shows us if we’re really getting our money’s worth Shows us if we’re really getting our money’s worth

or getting ripped offor getting ripped off

Bias/Sources of ErrorBias/Sources of Error

The broken cookies in some of the The broken cookies in some of the packagespackages

Even though each individual package Even though each individual package was weighed on the same scales, two was weighed on the same scales, two different scales were used throughout the different scales were used throughout the whole experimentwhole experiment

Had to estimate ourselves the average Had to estimate ourselves the average number of expected cookies per packagenumber of expected cookies per package

Conclusions/OpinionsConclusions/Opinions

We conclude that the 100 calorie packs are not 100 We conclude that the 100 calorie packs are not 100 calories because the actual average weight in grams is calories because the actual average weight in grams is higher that the expected weight in grams. higher that the expected weight in grams.

We also conclude that the customer gets their money’s We also conclude that the customer gets their money’s worth and the number of cookies in each bag is worth and the number of cookies in each bag is relatively the samerelatively the same

We were very surprised to find that the average weight We were very surprised to find that the average weight in grams was higher than the expected weight. in grams was higher than the expected weight.